Observational equations

In reducing media, a synthetically useful variation of the Smiles rearrangement, which leads to the formation of fused ring systems, has been observed (equation 77)251. In this reaction, rearrangement is followed by displacement of the sulfinate anion by a nucleophilic o -substituent. 

Thus the key experimental observation Equation (7.11), is satisfied in presence of spillover. When an external overpotential AUWR is applied, with a concomitant current, I, and O2 flux I/2F, although UWR is not fixed anymore by the Nemst equation but by the extremally applied potential, still the work function Ow will be modified and Equations (7.11) and (7.12), will remain valid as long as ion spillover is fast relative to the electrochemical charge transfer rate I/2F.21 This is the usual case in solid state electrochemistry (Figs. 7.3b, 7.3d) as experimentally observed (Figs. 5.35, 5.23, 7.4, 7.6-7.9). 

The temperature-factor parameter B and the scale factor k were determined by a least-squares procedure/ with observational equations set up in logarithmic form and with weights obtained from those in equation (9) by multiplying by (G (obs.))2. Since a semi-logarithmic plot of G2 (obs.)/Gf (calc.) against B showed a pronounced deviation from linearity for the last five lines, these lines were omitted from the subsequent treatments. They were much broader than the others, and apparently their intensities were underestimated. The temperature-factor parameter B was found by this treatment to have the value 1-47 A2. 

Fifty-two observational equations were set up and reduced in the usual way to two normal equations,... 

The usual sulfone synthesis by displacement of halide by sulfmate is assumed to have a nucleophilic 8 2 mechanism However, in special cases of alkyl halides with additional, electron-withdrawing substituents a radical substitution pathway has been observed (equation 32). Correspondingly, substitutions under formation of sulfones take... 

First, we rewrite the constraint functions appearing in the observational equation (5) by taking explicitly into account the phase of the residual target structure factor ... 

Multiplication of the observational equations (5) by a factor exp(-i< >y), leads to the modified constraint functions,... 

Taking the real and imaginary parts of the left- and right-hand sides of the newly rewritten observational equation, one obtains... 

A relatively low potential, one-electron oxidation is observed (Equation (72)), followed above pH 2.2 by a two-electron oxidation, two-proton step (Equation (73)) and a one-electron oxidation (Equation (74)). In more acidic solutions a direct three-electron oxidation occurs leading also to the [Ruv O Ruv]4+ species. In various studies the Rulv O Rulv, RuIV-0 Ruv, and Ruv O Ruv species have been considered as the catalytically active form. Although these species have been characterized by resonance Raman and EPR spectroscopies,475,476,480 no definitive conclusion about the mechanism involved in the catalysis can be drawn and the question remains largely open. 

The extension of the same mechanistic reasoning to the corresponding thermal process (carried out in the dark) is not generally rigorous. Most commonly, the adiabatic electron-transfer step (kET) is significantly slower than the fast back electron transfer and follow-up reactions (fcf) described in Section 7, and the pseudo-steady-state concentration is too low for the ion-radical pair to be directly observed (equation 99). 

Methyl-l,2,4-triazole 37 undergoes radical alkylation to give monoalkylated 1-methyl-1,2,-4-triazoles 48a-e in which the new substituent is in the 5-position no addition products resulting from alkylation in the 3-position were observed (Equation 14 and Table 3) <2001TL7353>. 

When 3-(4-chlorofurazanyl-3-Ar(0)AT-azoxy)-4-nitrofurazan 218 reacts with weak bases and nucleophiles, selective attack on the carbon atom bonded to the nitro group occurs, but no products formed by substitution of the chlorine was observed (Equation 43) <2003CHE1357>. 

The product distribution observed in the dimerization of polyene-substituted ketyl radicals is also remarkable in that only products involving dimerization at the carbonyl carbon atom are observed (equation 23)82,83. This finding is quite independent of the reducing agent, since ketyl radicals formed by reduction with low-valent transition metal complexes behave analogously84-86. 

Homogeneous catalysts have been reported, which can oxidize methane to other functionalized products via C-H activation, involving an electrophilic substitution process. The conversion of methane into methyl bisulfate, using a platinum catalyst, in sulfuric acid, has been described. The researchers found that a bipyrimidine-based ligand could both stabilize and solubilize the cationic platinum species under the strong acidic conditions and TONs of >500 were observed (Equation (5)).13... 

The oxidation of />-toluenesulfonic acid to the corresponding alcohol and aldehyde was achieved using the Shilov system and when employing oxidants other than Pt(iv), including peroxydisulfate or phosphomolybdic acid, only moderate turnovers were observed (Equation (18)).28... 

The regiospecific functionalization of the terminal alkyl group of simple amines or ethers with bis(pinacolato)-diborane leads to organoboranes. The latter have manifold applications in organic synthesis since the catalytic borylation process can be combined with a functional group transformation step, including Suzuki-Miyaura couplings, for the synthesis of elaborated molecules. Curiously, functionalization of the C-H atoms a to the heteroatom was not observed (Equation (22)). a... 

Stereoselective catalytic cyclizations are now known, with excellent enantioselectivities observed (Equation (117)).106... 

Iridium hydride complexes effectively catalyze addition of nitriles or 1,3-dicarbonyl compounds (pronucleophiles) to the C=N triple bonds of nitriles to afford enamines.42S,42Sa Highly chemoselective activation of both the a-C-H bonds and the C=N triple bonds of nitriles has been observed (Equation (72)). To activate simple alkane dinitriles, IrHs(P1Pr3)2 has proved to be more effective (Equation (73)). The reaction likely proceeds through oxidative addition of the a-C-H bonds of pronucleophiles to iridium followed by selective insertion of the CN triple bonds to the Ir-C bond. 

The proposed catalytic cycle of the ruthenium-catalyzed intermolecular Alder-ene reaction is shown in Scheme 21 (cycle A) and proceeds via ruthenacyclopentane 100. Support for this mechanism is derived from the observation that the intermediate can be trapped intramolecularly by an alcohol or amine nucleophile to form the corresponding five-or six-membered heterocycle (Scheme 21, cycle B and Equation (66)).74,75 Four- and seven-membered rings cannot be formed via this methodology, presumably because the competing /3-hydride elimination is faster than interception of the transition state for these substrates, 101 and 102, only the formal Alder-ene product is observed (Equations (67) and (68)). 

A single but noteworthy example of a [2 + 2 + 2 + l]-cycloaddition reaction was reported by Takats and Cooke in 1997. In this process, Fe(CO)4(7]2-C2H2) reacts with acetylene to give an iron-tropanone complex in 26% yield (Equation (44)). When the analogous reaction was tried with substituted alkynes under an atmosphere of CO, iron-quinone complexes were observed (Equation (45)).168... 

Treatment of methylhexahydro-l//-pyrrolo[l,2- ]imidazole 60a with LiAlH4 in Et20 afforded a diol 61a in 87% yield, whereas similar treatment of 60b gave alcohol 61b in 98% yield. During the reduction, no ring opening was observed (Equation 7) <1998J(P1)2061>. 

In contrast to these transformations, Michael additions of simple enolates to acceptor-substituted dienes often yield mixtures of 1,4- and 1,6-addition products27-30. For example, a 70 30 mixture of 1,4- and 1,6-adducts was isolated from the reaction of the lithium enolate of methyl propionate with methyl sorbate30. This problem can be solved by using the corresponding silyl ketene acetal in the presence of clay montmorillonite as acidic promoter under these conditions, almost exclusive formation of the 1,4-addition product (syn/anti mixture) was observed (equation ll)30. Highly regioselective 1,4-additions... 

The formation of the bridged product 191 was investigated using the cyclopentadiene system as a model. Thus, the salt of the tosylhydrazone 198 was prepared and thermolyzed in order to examine three possible variants of rearrangements (equation 62)75. Analysis of the reaction products 200-202 and their transformations [e.g. the pyrolysis of bicyclic triene 202 to cA-8,9-dihydroindene 203 (equation 63) rather than to product 200 or 201] allows one to conclude that the mechanism involves a transformation of carbene 188 into diradical 204 which can be the precursor of all the products observed (equation 64)75. An analogous conversion takes place via radical 205 in the case of carbene 199 (equation 65). 

The reaction of (cyclobutadiene)metal complexes with X2 results in the oxidative decomplexation to generate either dihalocyclobutenes or tetrahalocyclobutanes. In comparison, substitution of (cyclobutadiene)MLn complexes 223 [MLn = Fe(CO)3, CoCp, and RhCp] with a variety of carbon electrophiles has been observed (equation 34)15. Electrophilic acylation of 1-substituted (cyclobutadiene)Fe(CO)3 complexes gives a mixture of regioisomers predominating in the 1,3-disubstituted product and this has been utilized for the preparation of a cyclobutadiene cyclophane complex 272 (equation 35)246. For (cyclobutadiene)CoCp complexes, in which all of the ring carbons are substituted, electrophilic acylation occurs at the cyclopentadienyl ligand. 

As it can be observed, equation (40a) represents the error-state observer, while (40b) is the internal model observer both are discrete systems that... 

In acetonitrile, a reversible couple is observed (Equation (40)) for trans-... 

Beckmann rearrangement of the oxime from 3-phosphonoalkylcyclohexenones 401 afforded lactams and regioselective migration of the non-unsaturated substituent was observed (equation 164). 

The A-heterocyclic ring of the alkaloid Stenine 406 was made by the use of a ring-expansion reaction and a high-yield lactam 405 formation was observed (equation 168). 

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